Dynamical scaling near the pseudogap quantum critical point of the two-dimensional Hubbard model
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909044019560448 |
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| author | Pelz, Mathias Kotliar, Gabriel von Delft, Jan Gleis, Andreas |
| author_facet | Pelz, Mathias Kotliar, Gabriel von Delft, Jan Gleis, Andreas |
| contents | We study dynamical scaling in the quantum-critical fan of the pseudogap-metal to Fermi-liquid transition of the two-dimensional Hubbard model. Using a four-patch dynamical cluster approximation with the numerical renormalization group as a cluster impurity solver, we access real-frequency dynamics over several decades at arbitrary temperatures. Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit $x=ω/T$ scaling of the form $χ''(ω,T)\sim \tanh(x/2)$, and the cluster contribution to the optical conductivity obeys $Tσ'_{\mathrm{cl}}(ω,T) \sim \tanh(x/2)/x$, implying a $1/T$ cluster dc conductivity. In the scaling regime, the vertex contribution to the cluster optical response is much larger than the bubble contribution. We further find evidence for a marginal-Fermi-liquid nodal self-energy. This, together with the $1/T$ vertex contribution to the conductivity, implies strange-metal optical transport in the quantum critical region. Our results describe several qualitative aspects of several experimental observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15060 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamical scaling near the pseudogap quantum critical point of the two-dimensional Hubbard model Pelz, Mathias Kotliar, Gabriel von Delft, Jan Gleis, Andreas Strongly Correlated Electrons We study dynamical scaling in the quantum-critical fan of the pseudogap-metal to Fermi-liquid transition of the two-dimensional Hubbard model. Using a four-patch dynamical cluster approximation with the numerical renormalization group as a cluster impurity solver, we access real-frequency dynamics over several decades at arbitrary temperatures. Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit $x=ω/T$ scaling of the form $χ''(ω,T)\sim \tanh(x/2)$, and the cluster contribution to the optical conductivity obeys $Tσ'_{\mathrm{cl}}(ω,T) \sim \tanh(x/2)/x$, implying a $1/T$ cluster dc conductivity. In the scaling regime, the vertex contribution to the cluster optical response is much larger than the bubble contribution. We further find evidence for a marginal-Fermi-liquid nodal self-energy. This, together with the $1/T$ vertex contribution to the conductivity, implies strange-metal optical transport in the quantum critical region. Our results describe several qualitative aspects of several experimental observations. |
| title | Dynamical scaling near the pseudogap quantum critical point of the two-dimensional Hubbard model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.15060 |